Redbelt problem solving

In the movie Redbelt, Chiwetel Ejiofor plays Mike Terry, a Jiu Jitsu instructor who will fight but will not compete. He will fight in a real fight if necessary, but he won’t fight in a ring because competitions have arbitrary rules. He is a skilled fighter because he is creative, and competitions take away that creativity. At one point in the movie, someone Terry if he teaches people to win. He says no, he teaches people to prevail. In his mind, you can’t “win” a fight. A fight is a problem to be solved.

Mike Terry’s distinction between fights and contests makes me think of the distinction between practical and academic problem solving. Practical problem solving does not have arbitrary constraints whereas academic problems often do: you can use this technique but not that one, you can use this reference but not that one, etc. These academic limitations serve a purpose in their context, but sometimes we can imagine these constraints are still on us after we leave the classroom.

Sometimes we’ll struggle mightily to solve a problem analytically that could be easily be solved numerically (or vice versa). Or we’ll imagine that a problem must be solved using a particular programming language even though it could be done more easily using a different language. It feels like “cheating” to go for the easier solution. But if you’re not in an academic setting, you can’t “cheat.” (Of course I’m not talking about violating ethical standards to solve a problem, only dismissing artificial restrictions. Where there is no law, there is no sin.)

There may be good reasons for pursuing the more difficult solution, such as entertainment value. But often we do things the hard way for no good reason other than not having examined our self-imposed limitations. Maybe we’re trying to win rather than solve the problem.

My friend Andy worked in the Statistics and Business Research Department of the British Post Office for many years. He told me that one of the questions he was asked at the original job interview was “How would you take a random sample of letters from a mailbag”. (He was applying for a post as Assistant Statistician.) He immediately replied that he would tip the bag onto the floor, swish the letters around for a while then grab a handful. This was the right answer and it got him the job, but he was told that that question was notorious for completely flummoxing stats graduates. You can see why. They are thinking “Is a rigorous answer required or a quick-and-dirty one?” which is another example of not knowing what constraints to apply.

In order to justify my efforts over the past several years – The academic constraints have occasionally shown me why a particular approach does not work or is less optimal than the real-world approach might be. I claim that this sharpens my tool set.

I am reminded of a legendary story about Niels Bohr. As student he was ask how to determine the height of building using a barometer. Instead of the answer the instructor expected, he proceed to propose several alternative solutions including trading the barometer to the building super in exchange for the information and throwing the barometer off of the roof and seeing how long it took to hit the ground!

I think there are always constraints, but different constraints in each situation. Following the proper academic rules for one, and solving the problem both correctly and efficiently on the other.

To continue the martial arts analogy, there is an art to solving problems. Judo and Akido, the peaceful “art” forms of Jujitsu and Akijitsu, are cooperative rather than competitive, because your partner (“Uke”) helps to perform the movement. This allows the freedom to learn and fully explore the art – examine different solutions to the problem – without causing harm. The “-jitsu” or practical fighting versions are very similar, except a bit of unfriendly persuasion is added to make an uncooperative partner do the movement, and so applying the art to the practical situation.

I would suggest that the art to problem solving involves knowing which constraints apply or should be applied to a given problem; you may want to avoid the difficult constraints, but take advantage of constraints that simplify the solution.

“When people think about creativity, they think about artistic work — unbridled, unguided effort that leads to beautiful effect. But if you look deeper, you’ll find that some of the most inspiring art forms, such as haikus, sonatas, and religious paintings, are fraught with constraints. They are beautiful because creativity triumphed over the “rules.” Constraints shape and focus problems and provide clear challenges to overcome. Creativity thrives best when constrained.”

I first saw this as a very young man when Bobby Fischer played Boris Spassky in 1972. Highly creative play in a highly constrained environment.

I’ve always found that it was the long term struggle to tackle new ideas and understand how things work at a deep level that brings the best insights. Sure, I’ll throw together a one-off to solve someone’s problem quickly, but given the chance I’d rather implement an algorithm myself. Who knows, you might find a way to make it perform better for your case and be able to publish a paper on it later.

I think this is one of the biggest differences between the way the “stupid business majors or MBA’s” are taught to think and the way STEM’s are taught to think. In other words, what we STEM’s should learn from the “lesser minds” in a different field.

Step one in solving a problem is to go back to steps zero and step negative one. What are my goals and are those really the right goals?

If you can narrow it down to a definitive goal (not possible in “relearning circuits http://www.johndcook.com/blog/2012/01/23/grokking-electricity/ because I want to understand the way the world works” — but sometimes possible in a business setting) then you may be able to avoid a lot of unnecessary work. As you’ve noted elsewhere, this philosophy is also part of the ethos of hacking and pure mathematics. Imagine row-reducing an augmented matrix by hand: do you follow an algorithm written for a computer, or do you look for the easiest mental arithmetic that gets you a zero?

I relate it to the famous “Blitzkrieg” in chess (where someone won in 3 moves). My chess instructor taught us to ask ourselves at the beginning of every turn “What is the object of the game of chess?” (Not to capture materiel, but to kill the king.) Always look first to see if you can already make the kill (or get close).